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SDE SIS epidemic models

Gray, Alison and Greenhalgh, David and Mao, Xuerong and Pan, Jiafeng (2012) SDE SIS epidemic models. In: Workshop on Stochastic Modelling in Ecosystems, 2012-06-11 - 2012-06-12, Glasgow. (Unpublished)

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Abstract

In this paper we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals $I(t)$. We then prove that this SDE has a unique global positive solution $I(t)$ and establish conditions for extinction and persistence of $I(t)$. We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases.

Item type: Conference or Workshop Item (Speech)
ID code: 41322
Keywords: Susceptible-infected-susceptible model, pneumococcus, gonorrhea, stationary distribution, basic reproduction number, persistence, extinction, stochastic differential equations, Brownian motion, Probabilities. Mathematical statistics
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 02 Oct 2012 11:05
    Last modified: 07 Dec 2013 14:19
    URI: http://strathprints.strath.ac.uk/id/eprint/41322

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